Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<iostream>
#include<cstdio>
#include<cstring>

const int N=201000;

int f[N],ans[N],pos[N];
int n;

void calc(int x)
{
	if(ans[x+1]==0)
	{
		if(pos[x]>pos[x+1])ans[x]=1,f[x]=x+1;
		else ans[x]=0,f[x]=-1;
	}
	else 
	{
		int y=f[x+1];
		if((pos[y]<pos[x] && pos[x]<pos[x+1])
		|| (pos[x]<pos[x+1] && pos[x+1]<pos[y])
		|| (pos[x+1]<pos[y] && pos[y]<pos[x]))
			ans[x]=ans[x+1],f[x]=y;
		else ans[x]=ans[x+1]+1,f[x]=x+1;
	}
}

int main()
{
	scanf("%d",&n);
	for(int i=1,x;i<=n;i++)
		scanf("%d",&x),pos[x]=i;
	ans[n]=0,f[n]=-1;
	for(int i=n-1;i;i--)
		calc(i);
	printf("%d\n",ans[1]);
	return 0;
}